Dr R Gundran

1. SAMPLING OF ANIMAL
POPULATIONS
Learning objectives
At the end of the training session, the participants should be able to:
1. Explain the difference between population and sample;
2. Describe the difference between a parameter estimate (‘statistic’) and the
corresponding parameter;
3. Discuss the reasons for sampling;
4. Provide justification for obtaining an adequate and representative sample;
5. Outline the steps in design of a sampling strategy;
6. Distinguish between probability and non-probability sampling;
7. Describe the non-probability and probability sampling methods;
8. Discuss the strengths and weaknesses of each sampling method;
9. Outline the appropriate approach to estimate sample size for studies with various
objectives; and
10. Perform actual calculation of sample sizes
INTRODUCTION
Veterinarians may want to know if disease is present or absent in certain places and get
information on the level of disease and the risk factors for disease. Ideally, obtaining
accurate information in a population would require that each member in the population
should be studied. This is called a census. Census can be unrealistic, impractical,
tedious, lengthy, extremely difficult and costly.
An alternative to census is sampling whereby a segment of the population, called the
sample, is observed for the purpose of describing, estimating or inferring information
about the total population from which the sample was selected. The sample provides the
data, i.e., statistics, for use in estimating the characteristics of the target population, i.e.,
the parameter.
Sampling should be designed to select samples that will accurately describe or represent
the characteristics of the total population from which they are selected. Hence, the
purpose of sampling is for the sample to reflect the characteristics of the population from
which it is drawn. Obtaining information from a well-planned sample gives nearly the
same information as a census at less cost, time and manpower.
1

2. 1. THE SAMPLING PROCESS
The sampling process starts with clearly defined objectives to guide the investigator in
the conduct of sampling. Such objectives should contain the parameter of the population
to be estimated and the unit of concern such as the individual or group. The parameter of
interest can be the disease frequency, population characteristics and production indices.
The sampling process also requires that the target population be adequately described as
to the nature of the data required, the geographic location of the population and time
period covered by the study. The target population refers to the aggregate of
individuals for which characteristics the investigator wants to know and for which the
results of the study will be applied. A study population is the population of individual
animals or group of animals from which the sample is drawn, or the actual population
that can be observed. Whether the study population is the same as or smaller than the
target population, the essential thing is that the study population should be representative
of the target population from which it was drawn so that results from the sample can be
generalized to the target population. The ability to generalize results from a sample to the
target population is called external validity. A representative sample is one that
mirrors the characteristics of the population from which it was obtained. A formal
probability sampling method helps ensure the representativeness of the sample.
Before sampling is carried out, the unit to be sampled in the study population, i.e.,
sampling unit, must be defined. This may be an individual animal or group (herd, farm,
flock, cage, litter, house, stable, region and epidemiologic unit). Together, sampling units
comprise the sampling frame. It must be complete and up-to-date for simple random
sampling and each unit must appear only once.
Note that even with the most careful sampling, data in the sample will be different from
the population parameter. The degree to which a sample might differ from the population
is called sampling error. Sampling error can be minimized by increasing sample size
and use of probability sampling method.
2. SAMPLING METHODS
Samples can be drawn from the population either by probability or non-probability
sampling. Probability (random) sampling is a formal, impartial way of sampling in
which every unit in the population has a known, equal non-zero chance of being included
in the sample, and that chance can be quantified. As such, representative samples are
likely to be obtained, and results of the study can be inferred to the population from
which the sample was derived. This is not true for non-probability sampling where no
formal process of selecting a sample is done and as such, every unit in a population does
not have an equal chance of being selected.
2

3. Because sampling of units is left to the investigator, non-probability sampling, cannot
estimate population parameters from sample statistics. Hence, the findings in the study
cannot be generalized from the sample to the target population.
The choice of the sampling method will depend on a number of factors, such as the
available sampling frame, how disperse the population is, how costly it is to study
members of the population and how the investigators will analyze the data.
The advantages and disadvantages of these two sampling methods are listed in Table 1.
Table 1 Advantages and disadvantages of probability and non-probability sampling
methods
Method Advantages Disadvantages
Probability
• Can specify the magnitude of the difference
between the sample statistics and the
population parameter
• Can calculate precision of estimates
• Minimizes sampling error
• Findings can be generalized to the target
population.
• Difficult, expensive, more
complex and time-consuming
Non-
probability
• Cheaper & less time-consuming
• Easy to do
• Used when sampling frame is not available
• Often used in exploratory studies and analytic
studies
• No real confidence in the
accuracy of sample estimates
• Estimates can be biased and
extremely variable
The next section described features of both types of sampling method and detailed some
of the methods related to each type.
2.1 Probability Sampling
Table 2 presents the advantages and disadvantages of the five common types of
probability sampling method.
3

4. Table 2 Advantages and disadvantages of types of probability sampling methods
Type of
sampling
Advantages Disadvantages
Simple random
sampling (SRS)
• Easy to do • Requires a complete, updated
sampling frame of sampling units
• Can be unfeasible for large
populations and costly
Systematic random
sampling
• Easy to draw and a lot faster
than using SRS
• No need for a complete prior
knowledge of sampling frame
before sampling
• Danger that the sampling frame
may arrange subjects in a pattern.
Stratified random
sampling
• More precise estimates of the
parameter are obtained
compared to SRS
• Guarantees representation of all
strata in the sample
• Obtains estimates of outcomes
in each stratum
• Expensive and complex
• Requires advanced knowledge of
the status of sampling units in the
stratum and the stratification factor
Cluster sampling • Cheap, administratively efficient
• No need of sampling frame of
all units in the population
• Less precise estimate of the
parameter is obtained
• Requires more sampling units than
SRS
Multistage
sampling
• A complete sampling frame is
only needed in the first stage;
sampling frames are only
required for selected units in
subsequent sampling stage.
• Flexible and less costly than
SRS
• Less precise than SRS
• Requires more sampling units than
SRS
.
4

5. 2.1.1 Simple Random Sampling
Simple random sampling (SRS) is an impartial method of selecting the members of the
population in a way that each unit is equally likely to be chosen. Hence, an exhaustive
list of all members of the population of interest is required. It is simple and easy to do
using any of the following: drawing numbers from a box, flipping a coin, random-
numbers table, random number generators, computer-generated random numbers’ list.
Some epidemiology software packages such as Epi-Info and Survey Toolbox can be used
for this purpose.
5

6. 2.1.2 Systematic random sampling
Systematic sampling is random selection of sampling units at a pre-determined interval
after randomly selecting the first member as the starting point. The sampling interval is
determined by dividing the population size (N) by the required sample size (n).
The sampling frame can be a list of records from a computer file or a notational list such
as animals entering the killing floor of a slaughterhouse. By sampling in this manner, it
would not be necessary to obtain a comprehensive sampling frame prior to drawing the
sample provided the total number of sampling units is known and all the sampling units
or records are chronologically available.
Systematic random sampling
6

7. 2.1.3 Stratified Random Sampling
Stratified random sampling involves selection of sampling units from non-overlapping
subgroups called strata using SRS or other probability sampling method until the required
sample size is attained. Age, breed, sex, province or any other factor that influences the
variable of interest can be used as stratification variable. For example, for the study of
average sow mortality, sows can be stratified by breed, parity number, herd size,
geographic location, or any combinations thereof.
When the number of units is drawn from the strata proportional to the stratum size, the
method is called proportionate stratified random sampling. The probability of
selection uses the formula:
Stratum sample size = stratum size x sample size
Population size
This strategy is used when the herd size is known in advance: large herds are more likely
to be selected than small herds. In disproportionate stratified sampling, the numbers of
units are drawn from strata using different sampling fractions in the strata. A larger
percentage is taken from those bigger in size than others.
2.1.4 Multistage Sampling
Multistage sampling is sampling in two or more stages from within large groups and
selecting a sample from the cluster. In a two-stage sampling, samples of large groups (the
primary sampling unit) are selected randomly, followed by selection of a random sample
of secondary units from each chosen cluster.
Multistage sampling usually employs more than one probability sampling method and
sampling units can be selected with a probability proportional to their size. It is
particularly suitable in very large populations.
2.1.5 Cluster sampling
In cluster sampling, the population is divided into groups or clusters. A number of
clusters are selected randomly, and then all units within selected clusters are sampled.
The cluster or group is the sampling unit and the unit of concern. A group is a cluster of
animals. Examples of clusters are geographic areas, natural groups such as litters, pen,
herd, flock, cage, and geographic boundaries.
7

8. 8
Stratified simple random sampling using disproportionate sampling technique
In a flock of sheep that was vaccinated with an experimental liver fluke vaccine, you want to
estimate the proportion with serum antibody titers above 1:80. You determined that a sample
of 20 sheep is needed. Since breed can influence serum antibody response based on your
review of literature, you decided to carry out stratified random sampling by (1) listing the
sheep belonging to each breed and (2) taking a simple random sample of animals from each
breed. The sample size in each stratum is obtained by multiplying the total sample size with
the proportion in the herd belonging to each breed.

9. 9
Two-stage sampling
Suppose you want to determine the seroprevalence of paratuberculosis in carabaos in
municipality X. Because of logistical difficulties, you decided to conduct sampling in two
stages. Based on prior calculation, you determined that you have to sample 3 barangays
and 15 carabaos from each selected barangay. The sampling design is shown below:
Note that there is no need to have a list of all the carabaos in the 10 villages. All one needs
is a list of all carabaos from the 3 selected barangays. Admittedly, more information is
needed in this type of sample than what is required in cluster sampling. However, multi-
stage sampling still saves a great amount of time and effort by not having to create a list of
all of the units in a population.
For a three-stage sampling, you can get a list of all carabao herds in the selected barangays,
pick a random sample of carabao herds from each of those barangays, get a list of all the
carabaos in the selected herds and finally select a random sample of carabaos from each
herd. Each time a stage is added, the process becomes more complex.
Two-stage sampling
Suppose you want to determine the seroprevalence of paratuberculosis in carabaos in
municipality X. Because of logistical difficulties, you decided to conduct sampling in two
stages. Based on prior calculation, you determined that you have to sample 3 barangays
and 15 carabaos from each selected barangay. The sampling design is shown below:
Note that there is no need to have a list of all the carabaos in the 10 villages. All one needs
is a list of all carabaos from the 3 selected barangays. Admittedly, more information is
needed in this type of sample than what is required in cluster sampling. However, multi-
stage sampling still saves a great amount of time and effort by not having to create a list of
all of the units in a population.
For a three-stage sampling, you can get a list of all carabao herds in the selected barangays,
pick a random sample of carabao herds from each of those barangays, get a list of all the
carabaos in the selected herds and finally select a random sample of carabaos from each
herd. Each time a stage is added, the process becomes more complex.

10. 10
Please correct
Box 1 List all towns with carabao
population in the province
Box 2 Take a random sample of 4
herds per selected town
Two-stage cluster sampling
Suppose you want to do a seroprevalence study of bubaline paratuberculosis in your province
using a two-stage cluster sampling. Based on prior calculation, you determined that you have to
sample 3 towns, and 4 herds per selected town and collect blood from all carabaos in the
selected herds.
Two-stage cluster sampling
Suppose you want to do a seroprevalence study of bubaline paratuberculosis in your province
using a two-stage cluster sampling. Based on prior calculation, you determined that you have to
sample 3 towns, and 4 herds per selected town and collect blood from all carabaos in the
selected herds.

11. 2.2 Non-probability Sampling
In certain occasions, nonprobability sampling may be the only alternative because of cost,
speed, convenience, absence of complete sampling frame and practicality. Several types
of nonprobability samples are:
2.2.1 Convenience Sampling
Convenience sampling is based on the ready availability and easy accessibility of
sampling units to the investigator. Examples are sampling herds near main roads,
sampling cattle owned by university farm, and sampling herds with records. This method
is easy and often the only feasible one, particularly for those with restricted time and
resources for collecting information, and its use can be justified provided its limitations
are clearly understood and stated. It is often used in analytic studies.
2.2.2 Quota Sampling
Quota sampling is similar to stratified random sampling except that sample selection is
left to the investigator. Here, sampling is done until a specific number of units for various
subpopulations have been selected; there are no rules as to how these quotas are to be
filled.
2.2.3 Judgement Sampling
In judgment sampling, the investigator uses his “expert” judgement on the composition of
the sampling frame based on his knowledge of the population and his judgement that the
sampled units are typical of the population from which they come from.
2.2.4 Purposive Sampling
A purposive sample is one which is selected for a purpose by the investigator. This
method is often used to collect cases for the case series study or to select both cases and
controls if case-control study. It is often used in determining usage patterns of veterinary
services where areas chosen are those with high patronage in the past.
2.2.5 Haphazard sampling
This is a method in which the sample is made up of those that come at hand or
whichever animal is available.
11

12. 3. BIAS IN SAMPLING
Bias is a tendency of estimate to deviate in one direction from a true value. Bias in
sampling results to distortion of study results. It can occur during selection of sampling
units and in measurement of exposure or outcome. Examples are listed below:
Sampling bias can be due to: Measurement bias occurs when:
• Incomplete sampling frame
• Improper sampling
• Incomplete coverage
• Studying volunteers only
• Missing cases of short duration
• Non-response
• Not representative of the population
• Respondents do not tell the truth
• Respondents do not always understand
the questions.
• Respondents forget
• Respondents give different answers to
different interviewers.
• Respondents may say what they think the
interviewer wants to hear.
4. SAMPLE SIZE DETERMINATION
The size of the sample is crucial in epidemiology. In descriptive studies for example,
sample size will determine partly how close the sample will estimate the true population
value, i.e., accuracy. Too few samples yield inaccurate and imprecise estimates. Large
samples, though may be more accurate and precise in estimating the population
parameter, are costly and can be a waste of valuable resources when a smaller sample can
give nearly precise result at less cost than a large sample. Accurate and precise
determination of the parameter of interest should therefore be considered in sample size
determination.
Sample size determination should also consider the number of variables, availability of
sampling fame, the study objectives, type of probability sampling method used and
nonstatistical concerns such as cost, time, facilities and manpower. Large sample size is
required in studies of several variables and in studies using cluster and multistage
sampling.
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13. 4.1 Cost Consideration in Sampling
Cost of sampling is a major consideration in determining sample size. Cost involves
laboratory tests equipment, supplies, salaries of field staff, etc. The investigator should
therefore attempt to achieve the highest precision of the estimate at least cost using any of
the following:
(1) Specify precision of the estimate and then minimizing cost of sampling
The smallest sample size needed to attain this precision is taken.
(2) Specify the cost of sampling, and then maximizing the precision of the estimate
Here, the largest sample size possible is taken but there is a need to check if the
level of precision attained by this sample size is acceptable.
In SRS, there is little opportunity to save on costs, except in reducing the number of
sampling units studied. In stratified sampling, however, different numbers of units can
be selected from different strata, according to costs of sampling in each stratum. The
basic rule is to sample as few as necessary units from strata with high costs and to
increase the number of sampling units in strata with lower sampling costs. Cluster
sampling is less costly than SRS since the entire clusters are sampled, rather than
sampling individual units which can be widely dispersed in several herds. Multi-stage
sampling is the most flexible since the number of units at different stages can be varied
according to respective sampling costs.
4.2 Basic Applications
Sample size determination has several applications in epidemiology that includes disease
monitoring and surveillance. In disease monitoring, the disease is assumed to be present,
hence the objective is to determine its prevalence. In disease surveillance, cases of the
disease of interest are actively sought (1) to prove total freedom from disease or presence
of disease at or below a stated minimum prevalence, or (2) to confirm that a disease has
not been re-introduced. Therefore, sample size depends on the objectives of the study.
This chapter presents the procedures for sample size estimation of disease prevalence and
detection of the presence of disease. Sample size can be determined using appropriate
formulas, published tables of sample size and software packages. The choice of the
method will depend on several factors such as availability, feasibility, cost, convenience
and computer skill.
13

14. 4.2.1 Sample Size to estimate Disease prevalence
(1) Use of sample size formula for estimating disease prevalence (Martin et al., 1987;
Thrusfield, 2007).
(2) Tables of Sample Size to Estimate Prevalence
14
Calculating sample size in a descriptive study to estimate prevalence in a
population
Suppose we want to determine the prevalence of Disease Y in a 400-cattle herd. Since
we have no idea what is the expected prevalence in this population, we use P = 50%
and that we would like that our estimate to be within 5% (d) at 95% confidence level.
Thus:
n = 1.962
PQ = 1.962
0.50 (1-0.50) = 3.84 (0.0.25) = 0.96 = 384
d2
(0.05)2
0.0025 0.0025
Reduce the required sample size if n >10% of N, i.e., 384/400 = 96%. Thus,
n ( c ) = 384 = 196 animals are required for a simple random
1 + 0.96 or stratified sample in a descriptive study
Calculating sample size in a descriptive study to estimate prevalence in a
population
Suppose we want to determine the prevalence of Disease Y in a 400-cattle herd. Since
we have no idea what is the expected prevalence in this population, we use P = 50%
and that we would like that our estimate to be within 5% (d) at 95% confidence level.
Thus:
n = 1.962
PQ = 1.962
0.50 (1-0.50) = 3.84 (0.0.25) = 0.96 = 384
d2
(0.05)2
0.0025 0.0025
Reduce the required sample size if n >10% of N, i.e., 384/400 = 96%. Thus,
n ( c ) = 384 = 196 animals are required for a simple random
1 + 0.96 or stratified sample in a descriptive study
Formula for sample size estimating proportion in a population and
adjustment of required sample size when the population is small
(Thrusfield,2007)
The formula below is used to estimate proportion (e.g., prevalence, mortality, culling
rate) in a population.
where:
n = Required sample size
Zα
= Multiplier corresponding to a chosen confidence level. The confidence level is
the degree of certainty that the interval of the sample estimate includes the true
population value. By convention, 95% confidence level is used and the
multiplier is 1.96. Since 95% is more commonly used, we can substitute 1.96
for zα. .
For 90% and 99% confidence levels, 1.645 and 2.576 are the multipliers,
respectively.
P = Expected prevalence derived from any of the following:
Prevalence from published studies, other related local surveys
Pilot study
Intelligent guess; expert opinion
50% (the level that requires the largest sample size)
Q = 1-P
d = Desired absolute precision
Arbitrarily set by the investigator. For example, an absolute error of ± 5% of a
prevalence of 10% represents an acceptable range of 5-15%.
Reducing the required sample size using finite population correction
factor
When sampling a relatively small population, the required sample size can be
adjusted using the finite population correction factor:
n ( c ) = n Required sample size
1 + f 1 + Sampling fraction
Where sampling fraction (f) = n Sample size
N Population size
The correction factor is applied only in descriptive studies using simple or stratified
random sample and when the sampling fraction is greater than 10% of the population
size.
Formula for sample size estimating proportion in a population and
adjustment of required sample size when the population is small
(Thrusfield,2007)
The formula below is used to estimate proportion (e.g., prevalence, mortality, culling
rate) in a population.
where:
n = Required sample size
Zα
= Multiplier corresponding to a chosen confidence level. The confidence level is
the degree of certainty that the interval of the sample estimate includes the true
population value. By convention, 95% confidence level is used and the
multiplier is 1.96. Since 95% is more commonly used, we can substitute 1.96
for zα. .
For 90% and 99% confidence levels, 1.645 and 2.576 are the multipliers,
respectively.
P = Expected prevalence derived from any of the following:
Prevalence from published studies, other related local surveys
Pilot study
Intelligent guess; expert opinion
50% (the level that requires the largest sample size)
Q = 1-P
d = Desired absolute precision
Arbitrarily set by the investigator. For example, an absolute error of ± 5% of a
prevalence of 10% represents an acceptable range of 5-15%.
Reducing the required sample size using finite population correction
factor
When sampling a relatively small population, the required sample size can be
adjusted using the finite population correction factor:
n ( c ) = n Required sample size
1 + f 1 + Sampling fraction
Where sampling fraction (f) = n Sample size
N Population size
The correction factor is applied only in descriptive studies using simple or stratified
random sample and when the sampling fraction is greater than 10% of the population
size.

15. Sample sizes are provided in some textbooks (Canon & Roe, 1982). Tables of
approximate sample sizes to estimate proportion in a population are given for
90%, 95% and 99% confidence limits, range of expected prevalence and different
levels of desired accuracy. An example is shown in Table 3 which can be used if
the population size is large in relation to the sample. The sample sizes are derived
using the same formula as above.
15

16. Table 3 Table of sample size for estimation of proportion in a population at fixed
levels of confidence and accuracy and varying expected proportion
Level of Confidence
Expected
Prevalence
90%
Desired absolute
precision
95%
Desired absolute
precision
99%
Desired absolute
precision
10% 5% 1% 10% 5% 1% 10% 5% 1%
10% 24 97 2435 35 138 3457 60 239 5971
20% 43 173 4329 61 246 6147 106 425 10616
30% 57 227 5682 81 323 8067 139 557 13933
40% 65 260 6494 92 369 9220 159 637 15923
50% 68 271 6764 96 384 9604 166 663 16587
60% 65 260 6494 92 369 9220 159 637 15923
70% 57 227 5682 81 323 8067 139 557 13933
80% 43 173 4329 61 246 6147 106 425 10616
90% 24 97 2435 35 138 3457 60 239 5971
16

17. Use of a table of sample size for sample size estimation of proportion in
a population
Suppose we have a population of 1127 animals and we would like to estimate the
prevalence of a disease in a herd to within 5% of 40% expected prevalence at 95%
confidence level. To determine the sample size for a simple or stratified random sample
using the table provided below,
Find the row in column 1 where 40% expected prevalence is. Across this row, find the
column for 5% accuracy at 95% confidence level. The value where the row and column
meets is the required sample size. This value is 369. Therefore, 369 animals are
required. to estimate prevalence.
We can reduce this sample size using the finite population correction provided n
> 10% of N. Since 369 is 32.7% (369//1127) of the population size, we apply the
finite population correction:
n ( c ) = 369 = 369 = 278 animals would be sufficient
1 + 0.3273 1.3274
Use of a table of sample size for sample size estimation of proportion in
a population
Suppose we have a population of 1127 animals and we would like to estimate the
prevalence of a disease in a herd to within 5% of 40% expected prevalence at 95%
confidence level. To determine the sample size for a simple or stratified random sample
using the table provided below,
Find the row in column 1 where 40% expected prevalence is. Across this row, find the
column for 5% accuracy at 95% confidence level. The value where the row and column
meets is the required sample size. This value is 369. Therefore, 369 animals are
required. to estimate prevalence.
We can reduce this sample size using the finite population correction provided n
> 10% of N. Since 369 is 32.7% (369//1127) of the population size, we apply the
finite population correction:
n ( c ) = 369 = 369 = 278 animals would be sufficient
1 + 0.3273 1.3274
17
Expected
Prevalence
Level of Confidence
95%
Desired absolute precision
10% 5% 1%
10% 35 138 3457
20% 61 246 6147
30% 81 323 8067
40% 92 369 9220
50% 96 384 9604
60% 92 369 9220
70% 81 323 8067
80% 61 246 6147

18. (3) Use of Software Packages
The formulas describe above are only approximate. Epidemiology software packages
like WinEpiscope calculate sample sizes using exact formulas.
18
Determining the sample size using WinEpiscope
WinEpiscope was used to determine the sample size to estimate animal-level prevalence in
1127 animals where expected prevalence was 40%, accepted error was 5% at 95%
confidence level. The number of samples required is 369 animals. Adjusting the sample
size, 278 animals are needed.
Determining the sample size using WinEpiscope
WinEpiscope was used to determine the sample size to estimate animal-level prevalence in
1127 animals where expected prevalence was 40%, accepted error was 5% at 95%
confidence level. The number of samples required is 369 animals. Adjusting the sample
size, 278 animals are needed.

19. 4.2.2 Detecting disease or Confirming the Absence of Disease
To be sure that disease is present, all members of the population should be tested.
However, this is costly and impractical. Hence, sampling is done. Sampling to
detect disease is different from sampling to detect prevalence. The sample size
should be sufficient enough to find at least one animal with the disease in the
population. Formulas, tables of sample size and software packages can be used
for sample size determination.
(1) Use of Sample Size Formula
(2) Sample Size Estimation Using Tables To Detect Presence Of Disease
Tables of sample size serve as a quick guide in determining sample sizes compared to
performing calculations using formulas. Cannon & Roe (1982) provide tables of sample
sizes with P1 set at 0.95 and 0.99, for detecting at least one case of disease for various
19
Sample size calculation to detect disease
Suppose we have a leptospirosis-free herd of 250 pigs (N) and we want to be 95% (P1) sure
that it is free from Leptospira pomona. Based on data from an endemic area, L. pomona
normally affects 10% of the population (D). We want to know how many pigs are required
for bacterial culture. Thus:
D = 0.10 x 250 = 25
n = {1 - (1 – P1)1/D
} x {N - D/2} + 1
n = (1 - (1 - 0.95)1/25
) x (250 - 25/2) + 1
= 0.1129 x 238.5
= 27
We need 27 pigs. If none of the 27 pigs tested had L. pomona, we can be 95% sure that
the prevalence of leptospirosis in this pig herd is < 10% and because of this, L. pomona is
not present in the herd.
Sample size formula for detecting disease or confirm the absence of disease in
a finite population
n = {1 - (1 – P1
)1/D
} x {N - D/2} + 1
where:
n = required sample size
N = population size
D = estimated minimum number of diseased animals in the population
(population size x minimum expected prevalence)
P1
= confidence level (usually 95%)
Sample size formula for detecting disease or confirm the absence of disease in
a finite population
n = {1 - (1 – P1
)1/D
} x {N - D/2} + 1
where:
n = required sample size
N = population size
D = estimated minimum number of diseased animals in the population
(population size x minimum expected prevalence)
P1
= confidence level (usually 95%)

20. expected prevalence values and population sizes. Table 4 is one example which shows
sample sizes required for detecting disease at 95% confidence level.
20
Table 4 Sample size required for detecting disease at 95% confidence level
(Canon & Roe, 1982)
Pop’n
size
(N)
(i) Percentage of diseased animals in population (d/N)
OR (ii) Percentage sampled and found clean (n/N)
50% 40% 30% 25% 20% 15% 10% 5% 2% 1% 0.5% 0.1%
10 4 5 6 7 8 10 10 10 10 10 10 10
20 4 6 7 9 10 12 16 19 20 20 20 20
30 4 6 8 9 11 14 19 26 30 30 30 30
40 5 6 8 10 12 15 21 31 40 40 40 40
50 5 6 8 10 12 16 22 35 48 50 50 50
60 5 6 8 10 12 16 23 38 55 60 60 60
70 5 6 8 10 13 17 24 40 62 70 70 70
80 5 6 8 10 13 17 24 42 68 79 80 80
90 5 6 8 10 13 17 25 43 73 87 90 90
100 5 6 9 10 13 17 25 45 78 96 100 100
120 5 6 9 10 13 18 26 47 86 111 120 120
140 5 6 9 11 13 18 26 48 92 124 139 140
160 5 6 9 11 13 18 27 49 97 136 157 160
180 5 6 9 11 13 18 27 50 101 146 174 180
200 5 6 9 11 13 18 27 51 105 155 190 200
250 5 6 9 11 14 18 27 53 112 175 228 250
300 5 6 9 11 14 18 28 54 117 189 260 300
350 5 6 9 11 14 18 28 54 121 201 287 350
400 5 6 9 11 14 19 28 55 124 211 311 400
450 5 6 9 11 14 19 28 55 127 218 331 450
500 5 6 9 11 14 19 28 56 129 225 349 500
600 5 6 9 11 14 19 28 56 132 235 379 597
700 5 6 9 11 14 19 28 57 134 243 402 691
800 5 6 9 11 14 19 28 57 136 249 421 782
900 5 6 9 11 14 19 28 57 137 254 437 868
1000 5 6 9 11 14 19 29 57 138 258 450 950
1200 5 6 9 11 14 19 29 57 140 264 471 1102
1400 5 6 9 11 14 19 29 58 141 269 487 1236
1600 5 6 9 11 14 19 29 58 142 272 499 1354
1800 5 6 9 11 14 19 29 58 143 275 509 1459
2000 5 6 9 11 14 19 29 58 143 277 517 1553
3000 5 6 9 11 14 19 29 58 145 284 542 1895
4000 5 6 9 11 14 19 29 58 146 268 556 2108
5000 5 6 9 11 14 19 29 59 147 290 564 2253
6000 5 6 9 11 14 19 29 59 147 291 569 2358
7000 5 6 9 11 14 19 29 59 147 292 573 2437
8000 5 6 9 11 14 19 29 59 147 293 576 2498
9000 5 6 9 11 14 19 29 59 148 294 579 2548
10,000 5 6 9 11 14 19 29 59 148 294 581 2588
∞ 5 6 9 11 14 19 29 59 149 299 598 2995

21. 21
Sample size estimation using table of sample size to detect presence of disease in a
population where the disease of interest is absent or its prevalence is minimally
low
Suppose we want to use a published table of sample size to determine the sample size
required to find out if Disease Y is not present in a disease-free population of 480. The
expected proportion of positives in this population is 2% and we want to be 95% certain
of detecting at least one positive animal.
Find the population size of 480 in column 1. Since there is none, we use 500, the
population close to 480. Look at the value across row of 500 that crosses the column of
the 2% percentage of diseased animals. This value is 129. Therefore, a sample of 129
animals is required to be 95% certain of detecting at least one positive.
Population
size (N)
(i) Percentage of diseased animals in population (d/N)
OR (ii) Percentage sampled and found clean (n/N)
50% 40% 30% 25% 20% 15% 10% 5% 2% 1%
10 4 5 6 7 8 10 10 10 10 10
20 4 6 7 9 10 12 16 19 20 20
30 4 6 8 9 11 14 19 26 30 30
40 5 6 8 10 12 15 21 31 40 40
50 5 6 8 10 12 16 22 35 48 50
60 5 6 8 10 12 16 23 38 55 60
70 5 6 8 10 13 17 24 40 62 70
80 5 6 8 10 13 17 24 42 68 79
90 5 6 8 10 13 17 25 43 73 87
100 5 6 9 10 13 17 25 45 78 96
120 5 6 9 10 13 18 26 47 86 111
140 5 6 9 11 13 18 26 48 92 124
160 5 6 9 11 13 18 27 49 97 136
180 5 6 9 11 13 18 27 50 101 146
200 5 6 9 11 13 18 27 51 105 155
250 5 6 9 11 14 18 27 53 112 175
300 5 6 9 11 14 18 28 54 117 189
350 5 6 9 11 14 18 28 54 121 201
400 5 6 9 11 14 19 28 55 124 211
450 5 6 9 11 14 19 28 55 127 218
500 5 6 9 11 14 19 28 56 129 225

22. Sample size determination to detect disease
Using either WinEpiscope and FreeCalc to determine the sample size needed to
detect at least one positive animal in a population of 250 at 95% level of
confidence and 10% as expected proportion of positives, 27 animals are required
assuming that the diagnostic test used is perfect. The maximum number of
positives that could be present and the level of confidence after testing a random
proportion of animals in a population of size (N) can likewise be determined.
(3) Use of Software Packages
One drawback of sample size formula for detecting disease is the assumption that
diagnostic test is perfect, i.e., no false positives and no false negatives! Since this
assumption is unrealistic, test sensitivity and specificity should be considered in sample
size estimation in order to increase the probability of detecting at least one true positive.
The software Freecalc (Cameron,1999) has this capability.
22

23. Sample size adjustment using FreeCalc program.
Since diagnostic test is imperfect, the required sample size needs to be adjusted.
Using FreeCalc, test sensitivity and specificity (95% and 98%, respectively) are
entered, along with the other data. The adjusted sample size obtained was 63.
Freecalc also shows the “cutpoint number of reactors”, the upper threshold
number of test-positive animals that can occur in the sample while still inferring
that disease is absent at the minimum specified prevalence. In this example, three
of 63 samples are considered to be false positives. If more than this number, the
evidence for freedom from disease is not as strong.
23

24. REFERENCES
Akhtar S, Riemann HP, Thurmond MC, Franti CE and Farver TB. 1990. The
Association between Serological Evidence of Exposure to Campylobacter fetus
and Productivity in Dairy Cattle. Preventive Veterinary Medicine 10:1-14.
Canon RM,and Roe RT. 1982. Livestock Disease Surveys: A Field Manual for
Veterinarians. Canberra: Australian Bureau of Animal Health.
Cameron, A. 1999. Survey Toolbox. ACIAR Monograh No. 54.
Dohoo I, Martin W and Stryhn H. 2003. Veterinary Epidemiologic Research.
Charlottetwon, Canada: AVC Inc. 705 pp.
Fleiss JL. 1993. Statistical Methods for Rates and Proportions. Toronto, Canada: John
Wiley and Sons.
Leech FB and Sellers KC. 1999. Statistical Epidemiology in Veterinary Science. New
York: MacMillan and Company.
James A.D. 1998. Guide to Epidemiological Surveillance for Rinderpest.
Rev.Sci.Tech.Off. Int.Epiz 17(3):796-809.
Pfeiffer D. 2002. Veterinary Epidemiology- An Introduction. Department of Veterinary
Clinical Sciences. The Royal Veterinary College, University of London.
Thrusfield M. 2007: Veterinary Epidemiology. 3rd
ed., Blackwell Science, Oxford,
England.
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25. EXERCISES
Exercise 1
You are a Provincial Veterinarian and the Bureau of Animal Industry has asked you to
provide an estimate of the seroprevalence of bovine brucellosis. You decided to conduct a
survey using random sampling.
The Epidemiology Unit of the Bureau requires a confidence level of 95% and an absolute
precision of the estimate of about ±2%. As no survey based on a representative sample of
the cattle population has been conducted previously, you are not sure what prevalence to
expect. The only data you have available is from serological examination of samples,
which had been submitted to the local diagnostic laboratories. These results indicate that
the serological prevalence over the last ten years varied between 5% and 13%. Assume
that no vaccination has been used. There are about 1000 herds in your province with a
total of about 1 million cattle.
Determine the sample size for estimating the seroprevalence of brucellosis. What
sampling approach would you use? What is the unit of interest and what is the sampling
unit? How would you construct a sampling frame?
Sampling approach
Unit of interest
Sampling unit
Assumed prevalence
Sample size
Five years after conducting a brucellosis eradication campaign based on test and
slaughter of animals, you were asked to find out if brucellosis is still present in the
population. How many animals should be serologically tested to be 95% confident that
there is no brucellosis reactor in the cattle population?
Answer:
Sample size
25

26. Exercise 2
Find the sample size required to estimate the prevalence in a large population in the
following table. Compute manually using the formula:
2
2
1.96 PQ
n
d
=
where:
n= required sample size
P= expected prevalence
Q= 1-P
d= desired absolute precision
Expected
Prevalence
Desired Absolute Precision
10% 5% 1%
10 35 138 3457
20
30
40
50
60
70
Exercise 3
At the serological surveillance in the FMD campaign, it was decided to sample pig herds
to ascertain if unvaccinated pigs had seroconverted, i.e., had been exposed to natural
infection. It is reasonable to assume that at least 5% of animals in such herds would be
seropositive. Therefore, a sampling protocol was designed to detect a seroprevalence of
5%. The level of confidence used was 95%.
If a herd of 200 animals was sampled, what is the sample size needed to detect at least
one seropositive animal in this herd with a probability of 0.95? Repeat the sample size
calculations for probabilities of 0.99, 0.90 and 0.80. All other conditions (e.g. N=200,
5%) remain the same. Interpret the results.
Sample Size Interpretation
99%
95%
90%
80%
26